Scaling behavior of linear polymers in disordered media

TL;DR

This paper challenges the conventional static averaging approach in modeling linear polymers in disordered media, demonstrating that kinetic averaging is essential for correct asymptotic scaling and providing detailed calculations of related exponents.

Contribution

It establishes the importance of kinetic averaging over static averaging for accurate scaling behavior and computes multiple critical exponents to two-loop order.

Findings

Kinetic averaging yields correct asymptotic scaling behavior.

Calculated critical exponents $ u_{ ext{SAW}}$, $ u_{ ext{max}}$, and multifractal exponents $ u^{(eta)}$.

Static averaging is insufficient for describing polymer scaling in disordered media.

Abstract

Folklore has, that the universal scaling properties of linear polymers in disordered media are well described by the statistics of self-avoiding walks Folklore has, that the universal scaling properties of linear polymers in disordered media are well described by the statistics of self-avoiding walks (SAWs) on percolation clusters and their critical exponent $\nu_{\text{SAW}}$, with SAW implicitly referring to \emph{average} SAW. Hitherto, static averaging has been commonly used, e.g. in numerical simulations, to determine what the \emph{average} SAW is. We assert that only kinetic, rather than static, averaging can lead to asymptotic scaling behavior and corroborate our assertion by heuristic arguments and a renormalizable field theory. Moreover, we calculate to two-loop order $\nu_{\text{SAW}}$, the exponent $\nu _{\text{max}}$ for the longest SAW, and a new family of multifractal exponents $\nu^{(\alpha)}$.